Final Review Math 1 Over Unit 3

Spring Final Review Math 1

Polygons

• A POLYGON is a closed figure with 3 or more straight sides.

• A REGULAR polygon has all equal side lengths and angle measures.

• If 2 polygons are CONGRUENT all corresponding side lengths are equal and corresponding angles are equal.

• 2 polygons are SIMILAR if all corresponding angles are equal and corresponding side lengths are PROPORTIONAL.

Multiple Choice

What is the best definition of a polygon?

• a triangle

• a closed figure with 3 or more straight sides

• any figure with 3 or more sides

• a polygon with all equal side lengths and angle measures

Multiple Choice

What is the definition of a REGULAR polygon?

• a triangle

• a closed figure with 3 or more straight sides

• any figure with 3 or more sides

• a polygon with all equal side lengths and angle measures

Multiple Choice

What is true about the corresponding ANGLE measures for 2 CONGRUENT polygons?

• They are equal

• They are proportional

Multiple Choice

What is true about the corresponding SIDE LENGTHS for 2 CONGRUENT polygons?

• They are equal

• They are proportional

Multiple Choice

What is true about the corresponding ANGLES for 2 SIMILAR polygons?

• They are equal

• They are proportional

Multiple Choice

What is true about the corresponding SIDES for 2 SIMILAR polygons?

• They are equal

• They are proportional

Multiple Choice

What is the same about both SIMILAR and CONGRUENT polygons?

• The sides are equal in length

• The sides are proportional

• The angles are equal measure

• The angles are proportional

Multiple Choice

What is different about SIMILAR and CONGRUENT polygons?

• Nothing, they mean the exact same thing.

• The sides are proportional are proportional for similar polygons but equal for congruent polygons.

• The angles are equal measure

• The angles are proportional

Classifying Triangles by their sides

• scalene- all 3 sides are different lengths

• isosceles- 2 of the sides are the same length

• equilateral- all of the sides are the same length

Multiple Choice

What is the definition of a scalene triangle?

• all 3 sides are the same length

• 2 of the sides are the same length

• all 3 sides are DIFFERENT lengths

Classifying triangles based on their angles

• Right- 1 angle that is exactly 90°

• Obtuse- 1 angle that is greater than 90°

• Acute- all 3 angles are less than 90°

Multiple Choice

Which type of triangle has a 90° angle in it

• obtuse

• acute

• right

Sum of the interior angles of a polygon

• To find the sum of the interior angles of any polygon is found by 180(n - 2) where n = # of sides.

• Example: Find the sum of the interior angles of a 18-gon.

• 180(16) = 2,880°

How to find EACH interior angle of a REGULAR polygon

• Find the total from 180(n - 2), then divide by # of sides

• Example: Find EACH interior angle of a regular octagon.

• 180(6) = 1080°

• /8 = 135°

Fill in the Blanks

Solving proportions

•  $\frac{x}{6}=\frac{7}{15}$  

• Cross multiply 15x = 42

• Then divide       $\frac{15x}{15}=\frac{42}{15}$  

• x = 2.8

Solving proportions with distributive property

•  $\frac{x+9}{12}=\frac{4x+7}{3}$  .

• 3(x+9) = 12(4x + 7)

• 3x + 27 = 48x + 84

• 27 = 45x + 84

• -57 = 45x

• x = -1.266666...

4 Shortcuts for Triangle Congruence

• SSS

• SAS

• AAS

• ASA

Multiple Select

Which of the following are shortcuts that prove 2 triangles are CONGRUENT? Check all that apply.

• AA

• ASA

• AAS

• SSA

• SSS

3 Shortcuts for Triangle Similarity

• SSS

• SAS

• AA

Multiple Select

Which of the following prove 2 triangles are similar? Check all that apply.

• AA

• SSS

• SSA

• SAS